The 25-year-old has also been linked with Manchester United, Liverpool, Barcelona and Real Madrid in recent weeks.
Llorente has previously admitted he is flattered by the interest shown in him by several of Europe’s biggest clubs.
“It’s a compliment that they are interested in me, that means I’m doing things right,” he said.
The People reports that City have made an enquiry about Llorente and could make a move for the striker next summer.
Llorente’s contract with Bilbao is set to expire in the summer of 2013.
